Vortex length

As illustrated in Fig. 5, the outer downwardly spiralling gas velocity decays as gas peels off into the inner upwardly spiralling exiting vortex. The length of this inner vortex, the natural vortex length, L, (Alexander, 1949) then represents the distance below the edge of the gas outlet tube below which no feed gas remains to peel off into the inner vortex. If the... 

Dp Particle diameter Dth Smallest particle able to cross width Lw El Collection efficiency at actual inlet loading E0 Collection efficiency at <1 gr/ft3 inlet loading H Cyclone height as defined in Fig. 6 L Natural Vortex Length... 

According to the convention in macroscale entry flow study, the vortex length has been widely used to characterize the vortical flow pattern observed in viscoelastic converging entry flow (see Eq. 8). The dimensionless vortex length is defined as the axial distance from the upstream contraction plane at which the primary flow first detaches from the wall to the upstream channel width. It can be expressed as... 

As Bryant et al. (1983) note, this equation seems incorrect, because as Dq gets smaller, it would be expected that Ly would get larger, not smaller as Eq. (13) predicts. Bryant et al. (1983) then developed an equation for the vortex length that seems more directionally correct ... 

Hoffman et al. (1995) studied the cyclone vortex length and found that separation efficiency was less for cyclones with their natural vortex ending in the cone instead of the barrel. They also reported that the vortex length (swirl intensity) deereased with increasing solids loading and was a strong function of the eyelone length. Akiyama and Marui (1989), in... 

Contraction coefficient for flow from the freeboard to the cyclone inlet Contraction coefficient for flow from the cyclone barrel to the cyclone outlet Solids loading, kg of sohds/m of gas Vortex length below gas outlet tube, m Cyclone inlet width, m Effective number of soUd spirals in a cyclone Reynolds number at the cyclone inlet based on... 

Hoffman AC, de Jonge R, Arends H, Hanrats C. Evidence of the natural vortex length and its effect on the separation efficiency of gas cyclones. FUt Sep 32 799, 1995. 

We note that such an effect of Dx on the vortex length is contrary to a well-known correlation for the vortex length, and also contrary to a nrunber of experimental observations, as will be discussed later... 

The position of the vortex end is difficult to model. The first and, by far, the best known relation for the natural vortex length i.e. the length from the lip of the vortex finder to the position of the end of the vortex) was proposed by Alexander (1949) ... 

The vortex length can be influenced by the presence of a vortex stabilizing plate or cone. 

The vortex length is increased by underflow (a bleed flow drawn from the dust hopper), and is shortened by gas backflow from the dust hopper (due to leakage, for instance). 

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